The method of external excitation for solving generalized Sturm–Liouville problems

摘要

A new numerical technique for solving the generalized Sturm–Liouville problem d2wdx2+q(x,λ)w=0, bl[w(0),λ]=br[w(1),λ]=0 is presented. In particular, we consider the problems when the coefficient q(x,λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling the physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues.The results of the numerical experiments justifying the method are presented.